Interactive visualizers

The core ideas of calculus are motions, not formulas. Each visualizer puts one idea under your finger. Paste any of them onto a class page from widgets. The default is the Riemann sum.

• Tangent Line Tracer: Watch the Derivative Appear

  Drag a point along f(x), watch the tangent rotate, and see f'(x) draw itself dot by dot. An interactive that shows what a derivative actually is.

• Riemann Sum Slider: Drag n, Watch the Error Vanish

  Drag the rectangle count from 1 to 200 and watch a left, right, midpoint, or trapezoidal Riemann sum converge to the exact integral as its error vanishes.

• Secant to Tangent: The Limit Definition, Made Physical

  Drag h to zero and watch a secant line pivot into the tangent. See how the difference quotient becomes f'(a), the limit definition of the derivative.

• Solid of Revolution Builder: Disk, Washer, and Shell

  Pick a region, watch it revolve into a 3D solid, and see the disk, washer, or shell volume integral build itself. Drag the bounds and check the volume.

• Related Rates Scene: Sliding Ladder and Cone Tank

  Drag a 10 ft ladder's base or a cone tank's water level and watch a related-rates derivation recompute dy/dt and dh/dt at that exact state.